feat(da): submitted batch size metric

[srene]

PR Standards

Opening a pull request should be able to meet the following requirements

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PR naming convention: https://hackmd.io/@nZpxHZ0CT7O5ngTp0TP9mg/HJP_jrm7A

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Close #1007

<-- Briefly describe the content of this pull request -->

For Author:

• [ ] Targeted PR against correct branch
• [ ] included the correct type prefix in the PR title
• [ ] Linked to Github issue with discussion and accepted design
• [ ] Targets only one github issue
• [ ] Wrote unit and integration tests
• [ ] All CI checks have passed
• [ ] Added relevant godoc comments

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For Reviewer:

• [ ] confirmed the correct type prefix in the PR title
• [ ] Reviewers assigned
• [ ] confirmed all author checklist items have been addressed

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After reviewer approval:

• [ ] In case targets main branch, PR should be squashed and merged.
• [ ] In case PR targets a release branch, PR should be rebased.

Summary by CodeRabbit

• New Features

  • Introduced enhanced logging for batch submissions, now including the size of the batch.
  • Added a new metric to track the size of the last submitted batch for improved performance monitoring.

• Bug Fixes

  • None identified in this release.

• Documentation

  • Updated descriptions for new logging and metric capabilities.